Question

question 20 of 25
there are 4 milligrams of a radioactive substance in a lab in month 1. each month, half of the radioactive substance loses its radioactivity. which graph matches this situation?
four graphs labeled a, b, c, d
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a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Analyze the initial value

The initial amount of the radioactive substance is \(4\) milligrams. So when \(n = 1\), \(y=4\).

Step2: Analyze the trend

Since half of the radioactive substance loses its radioactivity each month, the amount of the radioactive substance is decreasing. The function is of the form \(y = a\cdot b^{n}\), where \(a = 4\) (initial value) and \(b=\frac{1}{2}\) (decay factor). A decreasing exponential function.

Answer:

D. Graph D